Distributed Massive MIMO: A Diversity CombiningMethod for TDD Reciprocity Calibration

Cheng-Ming Chen1, Steve Blandino1,2, Abdo Gaber3, Claude Desset2,Andre Bourdoux2, Liesbet Van der Perre1, and Sofie Pollin1,2

1Departement of Electrical Engineering, KU Leuven, Belgium2IMEC, Kapeldreef 75, 3001 Leuven, Belgium

3National Instruments Dresden, GermanyEmail:cchen@esat.kuleuven.be

Abstract—Distributed massive multiple-input multiple-output(DM-MIMO) gives a higher spectral efficiency and enhancedcoverage area, compared to collocated massive MIMO (CM-MIMO). In general, for massive MIMO, time division duplexis preferable as it enables downlink (DL) precoding based onuplink (UL) channel estimation. A time division duplex (TDD)reciprocity calibration is then essential to compensate the gapbetween the UL-DL channels, which can be done completely inthe base station relying on sounding reference signals (SRS).For a collocated array, relying on mutual coupling betweenantenna elements, each SRS is received with sufficient powerin the array, enabling a reliable estimate of the calibrationcoefficients. Nevertheless, for DM-MIMO, much less power iscollected in distant inter-cluster antennas which degrades theaccuracy of the estimated calibration. In this paper, we proposea novel inter-cluster combining method (ICCM) which improvesthe signal-to-quantization-noise ratio (SQNR) of the SRS, andhence achieves a more robust calibration accuracy for practicalDM-MIMO systems. Our experimental results of two 32-antennaarrays distributed in an indoor environment show that ICCMoutperforms the existing state-of-the-art algorithms in the senseof lower DL error vector magnitude (EVM) by exploitingdiversity and array gain efficiently.

Index Terms—Distributed antenna arrays, large-scale antennasystems, massive MIMO, reciprocity calibration

I. INTRODUCTION

Massive MIMO (M-MIMO) is an emerging technologywhich is capable of greatly enhancing the spectral efficiencyby serving multiple users at the same time and frequency [1],[2]. To deploy the massive MIMO systems, two paradigmscan be considered (see, e.g., [3]–[7]): collocated M-MIMO(CM-MIMO), where the base station (BS) antennas are phys-ically limited to a confined array in the cell center, anddistributed M-MIMO (DM-MIMO), where the BS antennasare geographically deployed over the cell and connected witha high speed back-haul. The DM-MIMO system has severaladvantages compared to the CM-MIMO system such as betterdecorrelation of channels even for closely collocated users [8],enhanced coverage area and ease of network planning [9], [10].Nevertheless, in practice, more challenges should be addressedto implement and deploy a DM-MIMO than a CM-MIMOsystem. Those are the synchronization of distributed local-oscillators, amplifier non-linearities, non-ideal analog filters[11] and the critical time division duplex (TDD) reciprocity.

In massive MIMO, the number of BS antennas (hundreds toeven thousands) is several orders larger than the number ofsingle antenna mobile stations (MSs). Therefore, for TDD-based massive MIMO, it is more spectrally efficient to obtaindownlink (DL) channel state information (CSI) from reciprocaluplink (UL) CSI. Although the physical channel is reciprocal,the baseband-to-RF and the RF-to-baseband conversion chainsare generally not [16]. Using the UL CSI is not sufficient toguarantee the effectiveness of user separation in DL, and thusthe RF impairments should be compensated.

In this contribution, we concentrate on the practical realiza-tion of the TDD reciprocity calibration [13]. Thanks to the ideaprovided by Argos [15], the reciprocity calibration can be donepurely in the BS side and hence no cooperation from MSs isrequired. For a CM-MIMO system, in which the BS antennasare confined to a limited space, the power of the SRSs usedamong each of the antenna pairs is also in a limited range, andwe can obtain a very good signal-to-noise ratio (SNR) in theSRS during the TDD calibration. Therefore, a full array gen-eralized least square (FA-GLS) method [12], [14], is suitablefor solving the TDD calibration problem for a CM-MIMOsystem. In contrast, for a DM-MIMO system demonstratedin Fig. 1, where the BS antennas are dispersed into severalclusters, the FA-GLS method is infeasible for three reasons.First, a larger gain difference between intra-cluster pairs andinter-cluster pairs is observed, which causes a huge burden forfixed-point implementation; second, the huge gain difference,to some extent, leads to non-invertible matrix when solvingthe FA-GLS problem for DM-MIMO; third, more overheadsfor sending back the collected SRSs to the center processorare required to calculate the solution. The hierarchical basedcalibration method presented in [13] provides a good solutionto deal with the three aforementioned difficulties for the DM-MIMO system. However, in an arbitrary deployed DM-MIMOsystem, some anchor nodes were assumed in every cluster forthe relative inter-cluster calibration [12], [13], and in reality,the channel between inter-cluster anchor nodes may not bethe strongest. In addition to a large distance and path-loss, thechannel can be shadowed, suffer from fading or blocked byobstacles as illustrated in Fig. 1.

The main contributions of this paper are summarized in the

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Fig. 1: An illustration of the DM-MIMO system which consists offour distributed clusters of antenna arrays. The Orange arrows standfor sending the SRSs for inter-cluster calibration. Some possible fac-tors degrade the robustness of the inter-cluster reciprocity calibration.For instance, the non-face-to-face in normal lines of the antennapanels or fading in between the arrays degrade the SRSs qualityduring the inter-cluster calibration. (Note that for a theoretical reasonwe apply a different configuration than the experiment)

following:• A hierarchical calibration method has been adopted for

DM-MIMO. The novelty is in the proposed inter-clustercombining method (ICCM), where we rely on maximumratio combining (MRC) and maximum ratio transmission(MRT) to combine multiple SRSs coherently, enabling apower gain and diversity gain.

• The performance of different calibration methods hasbeen compared and evaluated practically using a MassiveMIMO testbed with 64 antennas.

• To the best of our knowledge, this is the first work tovalidate a real DM-MIMO system in DL.

The paper is organized as follows: the system model andthe elimination of channel mismatches is described in SectionII. Section III presents different calibration methods and theproposed ICCM. The results of the paper are summarized inSection IV, and finally Section V concludes the paper.

The notations in this paper are introduced as the following:Uppercase boldface A denotes a matrix while lowercaseboldface a indicates a column vector. An m×n matrix A canbe considered as a side-by-side stack of n column vectors,so we could write A = [a1 a2 ... an]. Superscripts T , Hand −1 mean the transpose, Hermitian and inverse operationof a matrix, respectively. Moreover, Tr(A) and ‖A‖2 are thetrace and `2 norm of matrix A, respectively. abs(A) denoteselement-wisely calculation of the absolute value of matrix A.A◦B indicates the Hadamard product of two matrices. Finally,the cardinality of a set B is denoted as card(B).

II. SYSTEM MODEL AND THE ELIMINATION OF CHANNELMISMATCHES

A TDD DL massive MIMO with M BS antennas andK single antenna MSs is considered in the system model.

With linear precoding, a signal from one subcarrier of the or-thogonal frequency division multiplexing (OFDM) modulatedsymbol is expressed as

s =√EsWx, (1)

where x ∈ CK comprises data symbols from an alphabet χ,and each entry has unit average energy, i.e., E

[‖xk‖2

]=

1, k ∈ {1, ...,K}, so the total transmitted power Es = K.W ∈ CM×K is the linear precoding matrix, where W =VΛ1/2, V ∈ CM×K , and Λ ∈ RK×K is a diagonal matrix.The precoding matrix W satisfies Tr(WHW) = 1 and keepsthe precoded vector s a per-antenna equal power constraintby Λ, hence the row ‖wk‖2 = 1/K, ∀k. In TDD reciprocitybased massive MIMO, the DL CSI in the BS is estimated fromthe UL training symbols of the MSs. To differentiate from DL,superscript ul is added for UL only; similarly, to differentiatefrom RF characteristic in the BS, superscript m is applied forthe MS only. The UL channel Hul ∈ CM×K and DL channelH are not reciprocal because of the transceiver mismatchesbetween the BS and MS. They are expressed as

Hul = RGulTm , H = RmGT, (2)

where G ∈ CK×M stands for the physical channel and Gul =GT within the coherence time; R = diag(r1, ..., rM ) andT = diag(t1, ..., tM ) are the frequency domain RF mismatchfactors in the receiver and transmitter, respectively. Due tothe RF mismatches, Rm and T do not equal to Tm and R,respectively. Hence, the precoding cannot effectively removethe inter-user-interference (IUI). In [15], it was shown that byright multiplying the transposed UL channel with an inverseof the estimated relative calibration matrix C = γT−1R forsome γ 6= 0, we get a diagonally scaled version of DL channel:

(Hul)TC−1 = 1/γTmGT. (3)

For example, as shown in the zero-forcing precoded signalreceived at the MSs ym ∈ CK , the IUI caused by RFmismatches is removed and can be expressed as

ym = γ√EsR

m (Tm)−1

Λ1/2x + nm , (4)

where nm is the independent identically distributed (i.i.d.)complex Gaussian CN (0 ,N0 ) noise. The arbitrary complexfactor γ and RF channel responses in the MSs can be com-pensated by the DL channel estimates.

In conclusion, a sufficient accurate estimator for the reci-procity calibration matrix C is required to cancel out IUI.Fortunately, the calibration can be fully carried out in the BS,and no participation from MSs is required.

III. ESTIMATORS OF RECIPROCITY CALIBRATION

The motivation of this paper is to further improve therobustness in the reciprocity calibration of the DM-MIMOsystem. The proposed ICCM is built on top of the hierarchicalbased calibration method in [13]. In this section, we introducefirst the calibration model between BS to BS antennas and thenthe FA-GLS algorithm. For DM-MIMO system, the calibration

method is further evolved to the hierarchical based approach.Finally, the proposed hierarchical based ICCM is introducedand some remarks are given to highlight the advantages ofICCM.

A. Sounding Reference Signal

To estimate the diagonal calibration matrix C, SRSs aresent sequentially. Each time, the ith antenna sends a SRSsequence in one OFDM symbol and the other M−1 antennasreceive. Let yi,j denote the signal received at antenna i whentransmitting at antenna j. Signal yi,j and yj,i received in bothdirections between i and j at each subcarrier are denoted as

[yi,jyj,i

]=[rigi,jtjsjrjgj,itisi

]+[ni,jnj,i

]⇒[ cj 0

0 ci

][ yi,jyj,i

]= rirjgi,j

[ sjsi

]+ n

, (5)

where the SRS si is constrained to have power ‖si‖2 =1, i ∈ {1 . . .M} and can be any predefined sequence in thefrequency domain, so for simplicity we assume it equals 1; thephysical channels gi,j equals gj,i within the coherence time1;ni,j and nj,i are again i.i.d. complex Gaussian CN (0 ,N0 )noise. To improve the signal quality of received SRSs, thereference antenna is usually the center antenna. Without lossof generality, we assume antenna 1 as the reference and setthe calibration factor c1 as a common factor γ. By isolatinga complex multiplicative γ from the calibration matrix C andstacking it in a vector format, we get c = [1, c2, ..., cM ]T .

B. Full Array Generalized Least Squares (FA-GLS) Algorithm

When the antennas are collocated in a confined array, theline-of-sight (LoS) mutual coupling are quite similar whichleads to similar signal to quantization noise ratio (SQNR)between any pair of neighboring antennas. Therefore, thecalibration coefficients can be estimated jointly by a FA-GLSalgorithm, and a joint cost function is formulated as [13]

Jcal(c) =∑i,j 6=i

|ciyj,i − cjyi,j |2 . (6)

After constraining c1 to 1, the LS closed-form solution isrepresented as

c = [1 − (AH1 A1)

−1AH1 a1]

T , (7)

where A = [a1 A1] , A1 is the rest M − 1 columns and A isformulated as

Ai,j =

{ ∑Mn=1,n6=j |yn,j |

2, i = j

−y∗i,jyj,i, i 6= j. (8)

1The duration of all M SRSs transmission should be limited to thecoherence time

C. Traditional Hierarchical (TH) Calibration Method

For distributed BS antennas, as the arrays are dispersed overa wide area, path-loss between inter-clusters is generally muchlarger than that within a cluster2. Therefore, an alternative ap-proach called traditional hierarchical (TH) calibration method[13] was proposed. Suppose that there are O clusters with anequal number of S antennas in each cluster, i.e., M = O · S.The idea behind TH is that for each distributed array, we applythe previous method from (7) to obtain intra-cluster calibrationcoefficients. Afterwards, a relative calibration concept comesin to calibrate the clusters with respect to each other.

To introduce the inter-cluster calibration method, let (i, o)be the ith antenna in the oth cluster. Suppose that we haveobtained the intra-cluster calibration factor (ci)o, the exactcalibration coefficient c(i,o) can then be approximated as

c(i,o) ≈ (ci)o.co, (9)

where co stands for the inter-cluster calibration coefficient. Todetermine the inter-cluster calibration coefficient co, we firstreformulate the received SRS between clusters as y(i,o),(j,p) toreplace (5), with the SRS be pre-multiplied by the intra-clustercalibration coefficient (ci)o,

y(j,p)(i,o) = r(j,p)t(i,o)g(j,p)(i,o)(ci)o + n. (10)

Particularly noteworthy, as the dynamic range of path-lossbetween intra-cluster and inter-cluster is significantly large inDM-MIMO, a second time of receive gain adjustment beforethe start of inter-cluster calibration is beneficial in improvingthe SQNR. We then define a set of $i,j paths3 in responsiblefor sending inter-cluster SRSs between cluster o and p. Finally,a joint inter-cluster cost function can be derived as

Jint =∑o,p 6=o

∑$i,j

∣∣coy(j,p),(i,o) − cpy(i,o),(j,p)∣∣2 , (11)

The corresponding A matrix to solve the inter-cluster LSproblem is given by

Ao,p =

{ ∑Oq=1,q 6=o

∑$i,j

∣∣y(i,q),(j,p)∣∣2 , o = p∑$i,j−y∗(i,o),(j,p)y(j,p),(i,o), o 6= p

. (12)

The inter-cluster calibration can be visualized in Fig. 2, wherenine antennas in each of the two clusters are presented. Here,two candidate antennas are chosen in each cluster to form atotal of four connections. Assigning more antennas in a clusterincreases SNR as formulated in (12) but it also decreases thesystem efficiency.

D. Hierarchical based Inter-Cluster Combining Method(ICCM)

In order to increase the quality of estimation in betweenthe distributed arrays, more candidate antennas have to beconsidered in the inter-cluster calibration. However, moreSRSs transmission also means more overhead. In addition, we

2Here we focus on several collocated sub-arrays in a DM-MIMO3If an equal number Scl ≤ S of antennas is selected in each cluster, the

number of paths is card($i,j) = S2cl between any two clusters.

Fig. 2: The inter-cluster calibration of TH method: Four connectionsare formed for inter-cluster calibration if Scl = 2 in one cluster.

should keep in mind that the coherence time of inter-clusterchannels should be much shorter than that of LoS channelswithin a cluster. Furthermore, there is no deterministic way ofchoosing candidate antennas as channels between inter-clustersubject to shadowing and fading.

The question is how to minimize the time overhead forsending SRSs while maximizing the signal quality. A novelfinding behind the proposed ICCM is that after intra-clustercalibration compensation, all elements in a cluster can repre-sent their cluster jointly and hence transmit or receive the SRScoherently to boost array and diversity gain.

We introduce ICCM by defining two kinds of clusters, i.e.,master and slave clusters. First, a master cluster broadcastsSRS from a single reference antenna to all antennas in slaveclusters. Next, each slave cluster sequentially transmits oneSRS by MRT with all antennas in that cluster back to themaster cluster. The key point is that MRT is a closed-loopMIMO technique, so the SRS transmitted by MRT can onlybe coherently combined in the corresponding master cluster.Until now, we build only the connection between one masterand the other slave clusters.

By assigning master clusters in an iterative way, the es-timation accuracy is further improved by establishing theconnections among all clusters. If we have O clusters ofarrays in the distributed system, a total of O − 1 iterationsare then required to make a complete interconnection. In theoth iteration, o ∈ {1, ...O}, the oth cluster is set as the mastercluster, and the rest O−o clusters with indices from (o+1)thto Oth are assigned as the slave clusters. An example offour antenna arrays sending the SRS in four steps in the firstiteration is demonstrated in Fig. 3. There are five antennas ineach array; red grid represents the transmit antenna and bluedownward-diagonal denotes as the receive antenna. Startingfrom the upper-left corner, one SRS is transmitted from thereference antenna in the master cluster to all antennas in theother slave clusters. Meanwhile, all antennas in each slavecluster receive the SRS from the master cluster and combinethe signal by MRC. Then, in step two to four, the slave clusterssequentially transmit SRSs back to the reference antenna inthe master cluster by MRT. With these four slots of SRSstransmission, the master cluster builds connections with theother three slave clusters. When all the inter-connections arecompleted, we get a cost function of the ICCM based inter-cluster calibration:

JICCM =∑o,p 6=o

∑$i

∣∣coβp,(i,o) − cpα(i,o),p

∣∣2 , (13)

where $i is a set of candidate antennas in the master cluster.

To save bandwidth and for simplicity, in this paper, it is setto be a single reference antenna, same as the one in the intra-cluster calibration. (we keep the summation in the function tobe more general) Moreover, the MRC combined signal,

βp,(i,o) =

S∑j=1

d(j,p),(i,o)y(j,p),(i,o) = dTp,(i,o)yp,(i,o); (14)

and the MRT signal α(i,o),p is derived as

α(i,o),p = r(i,o)(g(i,o),p ◦ tp)Tdp,(i,o) + n. (15)

where tp = [t(1,p)...t(S,p)]T and r(i,o) stand for the equivalent

transmit RF and receive RF impairments after intra-clustercompensation, respectively. The MRT and MRC share thesame combining coefficients, dp,(i,o). Nevertheless, if weapply traditional MRC, we will end up in losing the inter-cluster calibration coefficients. Explained briefly, we reviewagain the receive SRS in the master cluster:

y(j,p)(i,o) = r(j,p)t(i,o)g(j,p)(i,o) + n. (16)

When y(j,p)(i,o) is multiplied by its complex conjugate as thetraditional MRC does, phase of RF-impairment term r(j,p)t(i,o)is also canceled out. To solve this, we design a simple methodof calculating the MRC coefficients in three steps:• Find the index ζ of the maximum path in yp,(i,o), ζ =

argmaxj|yp,(i,o)|, where j is the antenna index in the slave

cluster p. We choose the maximum path to improve SNRand the accuracy of the estimate.

• Align the phase of all S paths to the strongest path ζ.We get the phase of the MRC coefficients ∠dp,(i,o) =∠y(ζ,p),(i,o)1 − ∠yp,(i,o), where 1 is an S × 1 all-onevector.

• Normalize the amplitude of MRC coefficients for a faircomparison to TH method when applying MRT from aslave cluster4. The normalized amplitude of the MRCcoefficients are abs(dp,(i,o)) = abs(yp,(i,o))/

∥∥yp,(i,o)∥∥2.Finally, we obtain the corresponding A matrix:

Ao,p =

∑Oq�o

∑$i

∣∣βq,(i,o)∣∣2 +∑Oqo

∑$i

∣∣α(i,o),q

∣∣2 , o = p∑$i−α∗(i,o),pβp,(i,o), o < p∑

$i−β∗o,(i,p)α(i,p),o, o > p

. (17)

Some remarks are given here:• Compare (12) and (17), ICCM combines the SRS in the

very inner loop of the summation. Suppose there is a bigdynamic range in the channel gain, ICCM is more robustin the quantization error. This can be observed from (15),the SRSs are combined over-the-air before the RF front-end.

• Under the same condition that both card($i,j) andcard($i) equal to 1 in TH and ICCM, respectively. Eachreceived SRS in ICCM is a combining of S paths, whichbenefits from both array and diversity gain.

4In a practical implementation, this is not essential. However, we appliedthis in our experiment section for a fair comparison to the TH method.

Fig. 3: First iteration in the inter-cluster calibration of ICCMalgorithm: Five antennas in each of the four clusters are demonstratedin this example. Red grid antennas transmit, blue downward-diagonalantennas receive and unfilled antennas keep idle. In the first sub-figure, the upper-left cluster plays as the master cluster, and only onereference antenna in the cluster transmits SRS. Meanwhile, the otherthree slave clusters receive SRS simultaneously. Each slave clustercombines the received SRS by MRC. Then, each slave cluster appliesMRT in the SRS to the master cluster sequentially in steps two tofour.

IV. EVALUATION OF CALIBRATION METHODS IN THEMASSIVE MIMO TESTBED

In order to exhibit the robustness of ICCM for DM-MIMOsystems, we validate the performance of the three algorithms,i.e., FA-GLS, TH and ICCM in the University of Leuven(KUL) massive MIMO testbed. A simulation based evaluationis not considered here, as there is no existing path-loss andmutual coupling models which consider both the inter-clusterand intra-cluster arrays. We target for a real distributed case,as we want to validate a big impact from the fixed-pointquantization when there is a larger inter-cluster path-losscompared to the intra-cluster mutual coupling. The effectof big difference in channel gain enables us to show theadvantages of ICCM over the other two methods.

A. Description of the Scenario

The experiment was conducted in the lab as shown inFig. 4. The KUL massive MIMO testbed is a 64 antennasversion of Lund’s [17]. The testbed were distributed intotwo subsystems and each of them were connected to a 32-element patch antenna array. The antennas were co-polarizedand arranged in the array with one-half wavelength spacingand were operated in 20 MHz bandwidth at 2.6 GHz. Thetwo antenna panels were perpendicular to each other and wereseparated by a distance of around 2 m. To enlarge the path-lossin between clusters, LoS paths were blocked by absorbers5.To synchronize both subsystems, a common source is usedto provide the sample clock and time alignment. Moreover,two MSs were placed in between and separated by around 30

5We could not separate the two subsystems even further to enlarge path-loss due to a hardware limitation, a PXIe connection is required to connectthe two.

cm. Even with only two MSs, if the channel is non-reciprocal,user separation would still be a challenge as we will see inthe results.

Fig. 4: A two 32-antenna DM-MIMO BS station in the lab. To enlargethe path-loss by blocking LoS in between the clusters, two absorberswere placed in between the arrays. By the time the reciprocitycalibration is done, the uncoded 64-QAM DL data will immediatelybe sent to the two MSs.

B. Intra-cluster Mutual Coupling and Inter-cluster Path-lossMeasurement

Measurement was conducted with KUL testbed to validatethe power difference between the mutual coupling within anarray and the path-loss between the two arrays. Fig. 5 showsthe measured mutual coupling with different antenna spacingsin an anechoic chamber and the lab. When the antennas areclose to each other, with one antenna spacing, we got quitesimilar results for the two environments. As antenna spacingincreases, a slightly higher power contributed from multipathswas observed in the lab. A higher variance in the collectedpower was also observed when the antenna spacing increasedin both scenarios. Consequence, it can be concluded thatwithin a cluster there is always a pair of neighboring antennaswhich share a very strong and similar level of mutual coupling.

We demonstrate the path-loss between the two clusters forall bi-directional 32×32×2 paths in Fig. 6. The measurementexhibits a big variance of about 17dB, which validates thatthe MRC and MRT are indeed beneficial in collecting thediversity gain. If we compare the peak power of mutualcoupling (−23dB) to the mean of the path-loss (−48dB), weget equivalently a difference of 4 bits in fixed-point precision.For hierarchical based approach, the impact should be smaller,as the automatic gain control (AGC) can be set separately forboth intra and inter-cluster calibrations.

C. Error Vector Magnitude (EVM) and Throughput Evaluation

As the RF-to-RF impairment is an unknown, we directlyvalidate the accuracy of reciprocity calibration by measuringthe EVM of the DL uncoded 64-QAM and the achievedthroughput. They were recorded simultaneously just afterfinishing the reciprocity calibration. A moving average witha window size of 25 seconds was applied to smooth out thecollected data. During the calibration, the reference antennaswere assigned to the center of both arrays. card($i,j) and

Antenna Spacing (λ)

1 1.5 2 2.5 3 3.5 4 4.5 5

Pow

er

of M

utu

al C

ouplin

g (

dB

)

-60

-55

-50

-45

-40

-35

-30

-25

-20

lab

anechoic chamber

Fig. 5: Intra-cluster mutual coupling measured at the 32 antennaarray in both the lab and anechoic chamber with the massive MIMOtestbed.

Path-loss (dB)

-70 -65 -60 -55 -50 -45 -40 -35

Pro

babili

ty d

ensity

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

Fig. 6: Inter-cluster path-loss measured between the two 32-antennaarrays in the indoor experimental scenario by the massive MIMOtestbed. To be comparable to the measured mutual coupling, theantenna gain is not excluded.

card($i) were both set to 1 for TH and ICCM, respectively.Moreover, the transmitter power PTX was configured to 0dBm and a fixed receiver gain was configured to 30dB. Fromthe measurement in Section IV-B, we know even for theweakest path, the SNR=PTX − 65 − (−95)=30dB6 shouldbe sufficient for calibration. However, the power differencebetween the strongest and the weakest path is around (65 −25 = 40dB), which means if the strongest path is not truncatedby the receiver, then the SQNR of the weakest one degrades40dB. Hence, the big dynamic range in the designed scenarioenables us to compare which algorithm is more robust tothe quantization error. In Fig. 7 and 8, we show that theEVM and throughput of the two MSs evolve over around8 minutes. Apparently, the proposed ICCM outperforms theothers in both MSs. ICCM recovers the SQNR by the arraygain, assuming we receive equally from the inter-cluster paths,then the SQNR is boosted by 10log10(32) = 15dB. In thisexperiment, ICCM actually boosted more SQNR by diversity,

6The noise level can be referred to [14], eq. (22)

as not all paths shared the same power from the measurement.Interestingly, the EVM degrades quite quick over time, andthe accuracy of the reciprocity calibration determines therecalibration period. Particularly noteworthy, though the EVMof TH method degrades much faster than GLS, the throughputof GLS drops faster than that of TH. A possible explanationfor this, as we only have two clusters, the accuracy of thereciprocity coefficients in the master cluster of the hierarchicalbased calibration methods is not dependent on the inter-clustercalibration; the larger path-loss between the two clusters onlyimpacts the accuracy in the slave cluster. Hence, an accurateestimation only in the master cluster influences the perfor-mance significantly. Though the performance in throughput ofTH and ICCM looks similar, the EVM of ICCM is better. Asa result, the ICCM can support higher modulation schemesand is thus a superior candidate for DM-MIMO systems.

Seconds

50 100 150 200 250 300 350 400 450 500

64Q

AM

EV

M (

%)

1.5

2

2.5

3

3.5

4

4.5

5

5.5

6

MS1 ICCM

MS2 ICCM

MS1 GLS

MS2 GLS

MS1 TH

MS2 TH

Fig. 7: EVM of uncoded 64-QAM after finishing the reciprocitycalibration at the BS.

Seconds

50 100 150 200 250 300 350 400 450 500

Thro

ughput (M

bits/S

ec)

12.2

12.4

12.6

12.8

13

13.2

13.4

13.6

13.8

MS1 ICCM

MS2 ICCM

MS1 GLS

MS2 GLS

MS1 TH

MS2 TH

Fig. 8: Throughput comparison of the two MSs receive uncoded 64-QAM in DL. Peak data rate per MS is 13.68 Mbits/s as around 1/7of the LTE frame time is occupied for DL.

V. CONCLUSIONS

In this paper, we have proposed a potential reciprocitycalibration algorithm called ICCM for DM-MIMO system.The big difference between intra-cluster mutual coupling and

inter-cluster path-loss was then validated in the KUL massiveMIMO testbed in an indoor scenario. Our results show thatICCM outperforms the other two state-of-the-art methods fromtwo different aspects. Compare to FA-GLS, the hierarchicalbased approach is more robust to a big dynamic range in chan-nel gain within and in between the sub arrays. Moreover, com-pare to TH, ICCM exploits channel diversity to improve theaccuracy of the inter-cluster calibration coefficients. Overall,hierarchical based ICCM is the best candidate for estimatingthe reciprocity calibration coefficients in DM-MIMO systems.

ACKNOWLEDGES

This work was partially funded by the a Flemish Herculesgrant, and by the European Union’s Horizon 2020 undergrant agreement no. 732174 (ORCA project) Furthermore,the authors would like to thank Mr. Gino Van Houdt for hissupport of assembling the KUL massive MIMO testbed.

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